430 DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 



representatives for m = 3, 4 is not surprising as their limit displaced values are 

 certainly observed and the change is in full agreement with what takes place in the 

 other elements. 



We shall assume in what follows that the preceding allocation is correct, in other 

 words the limit is 29964'20 + the line for m = 2 is 15846 + 2'5p, and that the series 

 belongs to the F type. In that case the mantissa of the limit and of the sequent are 

 both multiples of the oun. These mantissse are respectively 913165 3 l'92f and 

 787174 + 246p 987f As both are oun multiples, so must be their difference. This 

 difference is 



125991-246p + 68 = 70 



(0 

 = 70f (l78075-3-49p+'97) 



In which if WATSON is correct to nearest unit p is equally probable between '5. 



It is very unfortunate that here we have to deal with two uncertainties not 

 generally met with, viz., on the one hand the uncertainty as to the real value of the 

 atomic weight, and on the other the magnitude of the possible observation error in the 



o 



fundamental wave-length, which WATSON has only measured to the nearest Angstrom. 

 If this had been 'I, i.e., p = 'I, the above result would show that since S lies between 

 1789 and 1783, the multiple must be 70f without any doubt, and consequently S in 

 the neighbourhood of 1787. The vahie of ( is so small, that its term will not affect our 

 present reasoning. We have, however, to allow for this uncertainty and a value of 

 p = 7 makes the second multiple = 70f x 1783'2 with a possible S. In this case the 

 first multiple gives 70^-x 1789'55, or S just on the improbable limit and it might be 

 excluded. The result, therefore, is 



Equally possible, p< '5 > '5, multiple = 70g- and S between 1785'3 and 1788. 

 Improbable, but perhaps possible, p = 7, multiple may be 70f and S = 1783'L 

 Very improbable, p =1, multiple 70 J and S = 1783'6. 



But also the limit and sequent mantissae must also be oun multiples, now 



913165-31'92f = 512 (l783'52-'062) 



(2) 

 = 511(1787'016-'062) 



> 22) 



(3) 



It might occur to the reader that the last should be a multiple of A 2 . But if the 

 series is the analogue of the 1864XF, to which the foregoing argument has pointed, 

 it should have a line of order m = 1 (n about = 3260). This should show M (A a ). 



